Bandwidth Selection for High-Dimensional Covariance Matrix Estimation

• 成果类型: Article
• 署名作者: Qiu, Yumou; Chen, Song Xi
• 署名单位: University of Nebraska System; University of Nebraska Lincoln; Peking University; Peking University; Iowa State University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2014.950375
• 发表日期: 2015
• 页码: 1160-1174
• 关键词: regularization

摘要

The banding estimator of Bickel and Levina and its tapering version of Cai, Zhang, and Zhou are important high-dimensional covariance estimators. Both estimators require a bandwidth parameter. We propose a bandwidth selector for the banding estimator by minimizing an empirical estimate of the expected squared Frobenius norms of the estimation error matrix. The ratio consistency of the bandwidth selector is established. We provide a lower bound for the coverage probability of the underlying bandwidth being contained in an interval around the bandwidth estimate Extensions to the bandwidth selection for the tapering estimator and threshold level selection for the thresholding covariance estimator are made. Numerical simulations and a case study on sonar spectrum data are conducted to demonstrate the proposed approaches. Supplementary materials for this article are available online.